Strained Donor-Bound Excitons in $^{28}$Si

TL;DR

This study maps the D$^0$→D$^0$X transition in isotopically enriched $^{28}$Si for P, As, and Sb under tunable uniaxial stress and magnetic fields, enabling precise extraction of deformation potentials. By combining valley-repopulations, Pikus-Bir hole Hamiltonians, Zeeman interactions, and diamagnetic shifts, the authors report a donor-dependent, unusually large electron uniaxial deformation potential $Ξ_ ext{u}$ and a magnetic-field–dependent hole shear deformation potential $d$, with $d$ decreasing and saturating at high fields. Diamagnetic shifts are consistent with prior measurements, and Sb signals are modeled using P-derived parameters due to weak Sb signals. The results yield a refined parameter set essential for silicon quantum devices based on D$^0$X transitions and point to missing physics beyond linear deformation potential theory, such as higher-order strain terms and magnetic-field–strain couplings.

Abstract

We present a comprehensive experimental study of the neutral donor to donor-bound exciton transition (D$^0$$\rightarrow\,$D$^0$X) in isotopically enriched $^{28}$Si, focusing on the group-V donors P, As, and Sb under finely tuned uniaxial stress along the [100] and [110] crystal axes and magnetic fields from 3.5 mT to 1.7 T. From these measurements, donor-specific deformation potentials are extracted. The uniaxial electron deformation potential $Ξ_\mathrm{u}$ is found to be significantly larger than values reported for other states or transitions in silicon and shows a clear dependence on the donor species, indicating an increased sensitivity of the D$^0$X state to strain and central-cell effects. We also observe a magnetic field dependence of the hole shear deformation potential $d$, suggesting a more complex strain coupling mechanism than captured by standard theory. Diamagnetic shift parameters determined from Zeeman spectra show good agreement with earlier measurements. Our results provide a refined parameter set critical for the design of silicon quantum devices based on D$^0$X transitions.

Figures (11)

• Figure 1: Schematic of the experimental setup for the detection of Auger electrons generated by the recombination of optically excited D$^0$X under mechanically applied stress. a) Exploded view rendering of the sample and its surrounding elements. All components colored in yellow are manufactured from PEEK. b) Depiction including laser, magnet, cryostat, lock-in amplifier, and actuator.
• Figure 2: Schematic of energy levels involved in the D$^0$$\rightarrow\,$D$^0$X transition as a function of uniaxial compressive stress $\sigma$ and magnetic field strength $B_0$. Transitions are labeled following the usual convention Steger_2012, which reflects their energy ordering in a magnetic field without strain. Applied strain, however, can modify this ordering, as shown. Note that even though $m_\mathrm{h}$ is not a good quantum number in the presence of both strain and magnetic field, we still use it as a label for the hole states according to the high-field limit.
• Figure 3: Arsenic neutral donor to donor-bound exciton transition spectra (D$^0$$\rightarrow\,$D$^0$X) in isotopically enriched $^{28}$Si, observed by measuring the sample AC conductivity under varying uniaxial stress. The two panels correspond to stress applied along the [100] and [110] crystal axes, as labeled. Data is shown as 2D color plots using nearest-neighbor coloring without interpolation, and brighter colors indicate a stronger signal intensity. Grey regions indicate areas outside the acquired data range. The white dashed lines represent a global fit of deformation theory to an extended dataset, see text for details.
• Figure 4: Arsenic neutral donor to donor-bound exciton transition spectra (D$^0$$\rightarrow\,$D$^0$X) in isotopically enriched $^{28}$Si under varying uniaxial stress and external magnetic fields. Each panel corresponds to a unique combination of stress orientation ([100] or [110]) and magnetic field strength (1.0 T or 1.7 T), as labeled in the subplots. For details regarding color code and fitted lines, refer to the caption of Fig. \ref{['fig:As_35G']}.
• Figure 5: Variation of the hole deformation potential $d$ with the applied external magnetic field strength $B_0$. Our presented deformation potentials are the result of a global fit to a large data set of the D$^0$$\rightarrow\,$D$^0$X transition under various uniaxial stress and magnetic fields. We also include previous results measured by Lo et al.Lo_2015, Conti et al.conti_2024, and Karasyuk et al.PhysRevB.45.11736.